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<p><a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle">Eight Queens</a> puzzle
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <iostream></code><br />
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<code>#include <array></code><br />
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Include dependency graph for n_queens.cpp:</div>
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Namespaces</h2></td></tr>
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<tr class="memitem:db/dc0/namespacebacktracking"><td class="memItemLeft" align="right" valign="top">  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/dc0/namespacebacktracking.html">backtracking</a></td></tr>
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<tr class="memdesc:db/dc0/namespacebacktracking"><td class="mdescLeft"> </td><td class="mdescRight">Backtracking algorithms. <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:d3/da1/namespacen__queens"><td class="memItemLeft" align="right" valign="top">  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/da1/namespacen__queens.html">n_queens</a></td></tr>
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<tr class="memdesc:d3/da1/namespacen__queens"><td class="mdescLeft"> </td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle">Eight Queens</a> puzzle. <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a40ae0c7fd04eb20e7f3bff13fc6a5808"><td class="memTemplParams" colspan="2">template<size_t n> </td></tr>
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<tr class="memitem:a40ae0c7fd04eb20e7f3bff13fc6a5808"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d4/d3e/n__queens_8cpp.html#a40ae0c7fd04eb20e7f3bff13fc6a5808">backtracking::n_queens::printSolution</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, n >, n > &board)</td></tr>
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<tr class="separator:a40ae0c7fd04eb20e7f3bff13fc6a5808"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a5730b6683f6adcf5c5ef75cf53dc7160"><td class="memTemplParams" colspan="2">template<size_t n> </td></tr>
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<tr class="memitem:a5730b6683f6adcf5c5ef75cf53dc7160"><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d4/d3e/n__queens_8cpp.html#a5730b6683f6adcf5c5ef75cf53dc7160">backtracking::n_queens::isSafe</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, n >, n > &board, const int &row, const int &col)</td></tr>
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<tr class="separator:a5730b6683f6adcf5c5ef75cf53dc7160"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a0dbd7af47d87f0b956609fe9e3288ecb"><td class="memTemplParams" colspan="2">template<size_t n> </td></tr>
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<tr class="memitem:a0dbd7af47d87f0b956609fe9e3288ecb"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d4/d3e/n__queens_8cpp.html#a0dbd7af47d87f0b956609fe9e3288ecb">backtracking::n_queens::solveNQ</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, n >, n > board, const int &col)</td></tr>
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||
<tr class="separator:a0dbd7af47d87f0b956609fe9e3288ecb"><td class="memSeparator" colspan="2"> </td></tr>
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||
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d3e/n__queens_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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||
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle">Eight Queens</a> puzzle </p>
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||
<p>The <b>eight queens puzzle</b> is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. The eight queens puzzle is an example of the more general <b>n queens problem</b> of placing n non-attacking queens on an n×n chessboard, for which solutions exist for all natural numbers n with the exception of n = 2 and n = 3.</p>
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<dl class="section author"><dt>Author</dt><dd>Unknown author </dd>
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<dd>
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<a href="https://github.com/Panquesito7">David Leal</a> </dd></dl>
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||
</div><h2 class="groupheader">Function Documentation</h2>
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||
<a id="a5730b6683f6adcf5c5ef75cf53dc7160"></a>
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||
<h2 class="memtitle"><span class="permalink"><a href="#a5730b6683f6adcf5c5ef75cf53dc7160">◆ </a></span>isSafe()</h2>
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<div class="memitem">
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<div class="memproto">
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<div class="memtemplate">
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template<size_t n> </div>
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<table class="memname">
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<tr>
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<td class="memname">bool backtracking::n_queens::isSafe </td>
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<td>(</td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, n >, n > & </td>
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<td class="paramname"><em>board</em>, </td>
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</tr>
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<tr>
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||
<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const int & </td>
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<td class="paramname"><em>row</em>, </td>
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</tr>
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<tr>
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||
<td class="paramkey"></td>
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<td></td>
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||
<td class="paramtype">const int & </td>
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<td class="paramname"><em>col</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>Check if a queen can be placed on matrix </p><dl class="tparams"><dt>Template Parameters</dt><dd>
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<table class="tparams">
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<tr><td class="paramname">n</td><td>number of matrix size </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">board</td><td>matrix where numbers are saved </td></tr>
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<tr><td class="paramname">row</td><td>current index in rows </td></tr>
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<tr><td class="paramname">col</td><td>current index in columns </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd><code>true</code> if queen can be placed on matrix </dd>
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<dd>
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<code>false</code> if queen can't be placed on matrix </dd></dl>
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<div class="fragment"><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  {</div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keywordtype">int</span> i = 0, j = 0;</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  </div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="comment">// Check this row on left side</span></div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordflow">for</span> (i = 0; i < col; i++) {</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordflow">if</span> (board[row][i]) {</div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  }</div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  }</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  </div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="comment">// Check upper diagonal on left side</span></div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keywordflow">for</span> (i = row, j = col; i >= 0 && j >= 0; i--, j--) {</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordflow">if</span> (board[i][j]) {</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  }</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  }</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="comment">// Check lower diagonal on left side</span></div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordflow">for</span> (i = row, j = col; j >= 0 && i < n; i++, j--) {</div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">if</span> (board[i][j]) {</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  }</div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  }</div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  }</div>
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</div><!-- fragment -->
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</div>
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</div>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">void </td>
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<td class="paramname"></td><td>)</td>
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<td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>Main function </p>
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<div class="fragment"><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  {</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> n = 4;</div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<int, n></a>, n> board = {</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<int, n></a>({0, 0, 0, 0}),</div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<int, n></a>({0, 0, 0, 0}),</div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<int, n></a>({0, 0, 0, 0}),</div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<int, n></a>({0, 0, 0, 0})</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  };</div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  </div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  backtracking::n_queens::solveNQ<n>(board, 0);</div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span> }</div>
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<div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
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</div><!-- fragment -->
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</div>
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</div>
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<a id="a40ae0c7fd04eb20e7f3bff13fc6a5808"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a40ae0c7fd04eb20e7f3bff13fc6a5808">◆ </a></span>printSolution()</h2>
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<div class="memitem">
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template<size_t n> </div>
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<table class="memname">
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<td class="memname">void backtracking::n_queens::printSolution </td>
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<td>(</td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, n >, n > & </td>
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<td class="paramname"><em>board</em></td><td>)</td>
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<td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>Utility function to print matrix </p><dl class="tparams"><dt>Template Parameters</dt><dd>
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<table class="tparams">
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<tr><td class="paramname">n</td><td>number of matrix size </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">board</td><td>matrix where numbers are saved </td></tr>
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</table>
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</dd>
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</dl>
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<div class="fragment"><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  {</div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"\n"</span>;</div>
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||
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < n; i++) {</div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < n; j++) {</div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">""</span> << board[i][j] << <span class="stringliteral">" "</span>;</div>
|
||
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  }</div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"\n"</span>;</div>
|
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  }</div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  }</div>
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<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
|
||
</div><!-- fragment -->
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</div>
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</div>
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<a id="a0dbd7af47d87f0b956609fe9e3288ecb"></a>
|
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<h2 class="memtitle"><span class="permalink"><a href="#a0dbd7af47d87f0b956609fe9e3288ecb">◆ </a></span>solveNQ()</h2>
|
||
|
||
<div class="memitem">
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<div class="memproto">
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||
<div class="memtemplate">
|
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template<size_t n> </div>
|
||
<table class="memname">
|
||
<tr>
|
||
<td class="memname">void backtracking::n_queens::solveNQ </td>
|
||
<td>(</td>
|
||
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, n >, n > </td>
|
||
<td class="paramname"><em>board</em>, </td>
|
||
</tr>
|
||
<tr>
|
||
<td class="paramkey"></td>
|
||
<td></td>
|
||
<td class="paramtype">const int & </td>
|
||
<td class="paramname"><em>col</em> </td>
|
||
</tr>
|
||
<tr>
|
||
<td></td>
|
||
<td>)</td>
|
||
<td></td><td></td>
|
||
</tr>
|
||
</table>
|
||
</div><div class="memdoc">
|
||
<p>Solve n queens problem </p><dl class="tparams"><dt>Template Parameters</dt><dd>
|
||
<table class="tparams">
|
||
<tr><td class="paramname">n</td><td>number of matrix size </td></tr>
|
||
</table>
|
||
</dd>
|
||
</dl>
|
||
<dl class="params"><dt>Parameters</dt><dd>
|
||
<table class="params">
|
||
<tr><td class="paramname">board</td><td>matrix where numbers are saved </td></tr>
|
||
<tr><td class="paramname">col</td><td>current index in columns </td></tr>
|
||
</table>
|
||
</dd>
|
||
</dl>
|
||
<div class="fragment"><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  {</div>
|
||
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keywordflow">if</span> (col >= n) {</div>
|
||
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  printSolution<n>(board);</div>
|
||
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordflow">return</span>;</div>
|
||
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  }</div>
|
||
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  </div>
|
||
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="comment">// Consider this column and try placing</span></div>
|
||
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="comment">// this queen in all rows one by one</span></div>
|
||
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < n; i++) {</div>
|
||
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="comment">// Check if queen can be placed</span></div>
|
||
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="comment">// on board[i][col]</span></div>
|
||
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keywordflow">if</span> (isSafe<n>(board, i, col)) {</div>
|
||
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="comment">// Place this queen in matrix</span></div>
|
||
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  board[i][col] = 1;</div>
|
||
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  </div>
|
||
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="comment">// Recursive to place rest of the queens</span></div>
|
||
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  solveNQ<n>(board, col + 1);</div>
|
||
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  </div>
|
||
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  board[i][col] = 0; <span class="comment">// backtrack</span></div>
|
||
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  }</div>
|
||
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  }</div>
|
||
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  }</div>
|
||
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|
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